Danielle,
Another beautiful route is to go in Cottonwood Pass(out New or Old Army Pass) and into Miter Basin. Camping high in Miter Basin makes Whitney an easily accessible day hike over Crabtree Pass and up the south facing side of the canyon to the crest which is followed to Trail Crest, then on to the summit.
This route has some off trail hiking but much of the route is via user trails and is not technically difficult.
A short day one over Cottonwood Pass camping at Chicken Spring Lake or shortly thereafter. On day two make your camp at Sky Blue Lake or higher in Miter Basin. Day 3 do Whitney. Day 4 hike part way out, going over one of the Army Passes, with enough time to climb Langley, then camping at one of the Cottonwood Lakes. Day 5 out.
Whichever route you choose have a great trip.
John